question_answer

ABC is a given triangle. AD, BE and CF are altitudes of\[\Delta \,ABC\].

Assertion (A): \[(A{{B}^{2}}+B{{C}^{2}}+C{{A}^{2}})\] \[>\]\[(A{{D}^{2}}+B{{E}^{2}}+C{{F}^{2}})\]

Reason (R): \[(A{{E}^{2}}-A{{F}^{2}})+(B{{F}^{2}}-B{{D}^{2}})\] \[+\]\[(C{{D}^{2}}-C{{E}^{2}})=0\]

A)  Both Assertion A and Reason R are correct and Reason R is a correct explanation of Assertion A.

B)  Both Assertion A and Reason R are correct but Reason R is not the correct explanation of Assertion A.

C)  Assertion A is correct, Reason R is wrong.

D)  Assertion A is wrong. Reason R is correct.

E)  None of these